### Abstract

In projection-based model reduction (MOR), orthogonal coordinate systems of comparably low dimension are used to produce ansatz subspaces for the efficient emulation of large-scale numerical simulation models. Constructing such coordinate systems is costly as it requires sample solutions at specific operating conditions of the full system that is to be emulated. Moreover, when the operating conditions change, the subspace construction has to be redone from scratch. Parametric model reduction (pMOR) is concerned with developing methods that allow for parametric adaptations without additional full system evaluations. In this work, we approach the pMOR problem via the quasi-linear interpolation of orthogonal coordinate systems. This corresponds to the geodesic interpolation of data on the Stiefel manifold. As an extension, it enables to interpolate the matrix factors of the (possibly truncated) singular value decomposition. Sample applications to a problem in mathematical finance are presented.

Original language | English |
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Title of host publication | Numerical Mathematics and Advanced Applications : ENUMATH 2017 |

Editors | Florin Adrian Radu, Kundan Kumar, Inga Berre, Jan Martin Nordbotten, Iuliu Sorin Pop |

Publisher | Springer |

Publication date | 5. Jan 2019 |

Pages | 683-691 |

ISBN (Print) | 978-3-319-96414-0 |

ISBN (Electronic) | 978-3-319-96415-7 |

DOIs | |

Publication status | Published - 5. Jan 2019 |

Event | European Conference on Numerical Mathematics and Advanced Applications - University of Bergen, Voss, Norway Duration: 25. Sep 2017 → 29. Sep 2017 http://www.uib.no/en/enumath2017 |

### Conference

Conference | European Conference on Numerical Mathematics and Advanced Applications |
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Location | University of Bergen |

Country | Norway |

City | Voss |

Period | 25/09/2017 → 29/09/2017 |

Internet address |

Series | Lecture Notes in Computational Science and Engineering |
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Volume | 126 |

ISSN | 1439-7358 |

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### Cite this

*Numerical Mathematics and Advanced Applications: ENUMATH 2017*(pp. 683-691). Springer. Lecture Notes in Computational Science and Engineering, Vol.. 126 https://doi.org/10.1007/978-3-319-96415-7_63